It depends on what you mean by "highest".

• If you have enough light, then the first thing you should do is to reduce the ISO setting to the minimum, so that you can get as much light as possible on the sensor1. Lower ISO means less noise, more dynamics.

• If there is still enough light, then close the diaphragm a bit compared to its maximum possible aperture (unless you need a shallow depth of field). Most lenses have their optimal quality around 2 stops below their maximum aperture (e.g. an F/3.5 lens is usually best around F/7). It's just a rule of thumb, it obviously depends on the lens). Don't close it too much, the image gets blurry due to diffraction on large F-numbers.

Getting a fast shutter speed is good, but if you are not shaking your camera too much and the subject is not a racing car, you won't see any difference between "fast shutter speed" and "even faster shutter speed". A typical heuristic is to use 1/"focal length", e.g. 1/50s for a 50mm lens. But shooting at 1/1000 or 1/4000 for the same 50mm will not make any visible difference.

Also, as DetlevCM points out in comments, the best image is not always the sharpest: if the subject moves, then a bit of motion blur can be part of the composition and reflect the movement while freezing the movement completely with a fast shutter speed will give the image an artificial taste (DetlevCM already gave the example of a helicopter, but the same applies in many other conditions where the subject is moving fast).

Footnotes:

1. Strictly speaking, decreasing ISO does not automatically mean more light on the sensor, but in most cases it ends up being the case.